ct ct The Formula m is Untenable in Michelson’s Experiment Attributed to Yang Shi-jia (1) Translated by Yulan (2) (1) Jingchang Normal School, Gansu Province ,737100, China, [email protected] (2) Nickel and Cobalt Research Institute, Jinchuan Group Ltd, Gansu Province ,737102,China, [email protected] [Summary] The experiment of Michelson—Morley’s is considered as the decisive experiment, according which to judge whether “ether wind ” exists or not. Though the experiment has been done repeatedly for many times, it seems that the calculating method of the experiment hasn’t been studied carefully. I am interested in the method of the calculation and have been studied it for a long time then I found that the original algorithm of the experiment is ct ct ct ct wrong: Michelson’s experiment can’t be calculated by the formula m , and m should be used. In Michelson’s experiment, even if “ether wind” does exists, with the correct algorithm, ct ct m 0 . The interference stripe don’t move, and of course the movement of the interference stripe can’t be observed in the experiment. So，here comes a conclusion, Michelson’s experiment can not prove the inexistence of “ether wind ”. [Key word] Michelson’s experiment calculating mistake inexistence of the “ether wind” can’t be testified ⅠSufficient and Necessary Condition of the establishment of Formula ()()rr rr m 21 21 Shown in figure one: we can suppose that rrrr2112 , , two points S1 ， S2 send out the light ray, which spread to space, ()rr21 corresponds to point P, the ()()rr21 rr 21 correspond to point Prr ; (21 ) and ()rr21 correspond to different set of points. The numeric values of ()rr21 moves along with interference stripe; oppositely, interference stripe varies along with the numeric values of ()rr21 , Just as Young’s experiment. Only in this case, the formula I ()()rr rr m 21 21 is tenable, we get: Conclusion one：The number that interference stripe moves along with the change of the optical path length difference equals to the variable quantity of optical path length difference divided by the ()()rr21 rr 21 wavelength m only when the relationship between interference stripe and optical path difference ()rr21 is in one–one correspondence. Ⅱ The Light Route of Michelson’s Experiment is Closed Michelson’s experiment is different from Young’s experiment, the light route of Michelson’s experiment is closed. we may suppose that lll12in Michelson’s experiment. 22ll Fig two shows: t 22corresponds to point A, cvc1/ 22cvc(1 / ) 22ll Fig three: t 22 corresponds to point A also. cvc(1 / ) cvc1/ 22 Obviously, before and after the whole interferometer is turned by 90° in the experiment, ttt and correspond to the same set of point, and according to the formula 22 2 A1212 AAArr 2cos( 21 ) we know that the average light intensity of the interference stripe corresponding to tt and are the same, which means that the brightness of the Interference Stripe is the same .Therefore ,we get : Conclusion two: In Michelson’s experiment, tt and corresponds to the same observational interference stripe. Ⅲ The Difference between Michelson’s Experiment and Young’s Experiment Based on the foregoing, in Young ’s experiment, the interference stripe and the difference (r2 r1 ) is in II one–one correspondence; but in Michelson’s experiment, before and after the whole instrument is turned by 90°, optical path difference c tt and c , which is opposite number of each other, correspond to the same observational interference stripe. Therefore, the relationship between the interference stripe and the difference ()rr21 isn’t in one–one correspondence. So we get: Conclusion three: Michelson’s experiment doesn’t have the necessary condition for the formula ()()rr rr m 21 21is tenable. ()()rr rr Ⅳ The Formula m 21 21can’t be used in Michelson’s Experiment According to the conclusion three, Michelson’s experiment doesn’t have the necessary condition ()()rr rr for the formula m 21 21is tenable, therefore, in a other word, the formula ct ct m is untenable in Michelson’s experiment. So we get: ct ct Conclusion four: The formula m is untenable to Michelson’s experiment. Ⅴ The Correct Algorithm for Michelson’s Experiment Based on the foregoing, in Michelson’s experiment, the relationship between the interference stripe and the difference ()rr21 is not one–one correspondence, but the interference stripe and the absolute value of the difference ｜ rr21 ｜is in one–one correspondence, if and only if the｜ rr21 ｜ changes, the interference stripe moves. So we get: ct ct Conclusion five: The formula m is tenable in Michelson’s Experiment. Ⅵ Inexistence of the “Ether Wind” can’t be proved by Michelson’s Experiment. In Michelson’s experiment, lll1211 meter . 22ll t 22 cvc1/ 22cvc(1 / ) 2l 2l t c(1 v 2 / c 2 ) 2 2 c 1 v / c ct ct ∴ tt , substitute it into the formula m , we get: ct ct m 0 . III Therefore, in Michelson’s experiment, even if “ether wind” does exists, with correct calculation, ct ct m 0 . The interference stripe don’t move, so that the movement of interference stripe can’t be observed in the experiment. So we get: Conclusion six: Inexistence of the “ether wind” can’t be testified by Michelson’s experiment. Ⅶ The Discussion of ll12 Shown in diagram two, we can suppose that the distance from the mirror G to the mirror M1 isl1 , and the distance from the mirror G to the mirror M 2 is l2 , then 2l 2l 2l 2l t 1 2 t 1 2 2 2 c(1 v 2 / c 2 ) c(1 v 2 / c 2 ) 2 2 c 1 v / c c 1 v / c llll Ⅰ 22 1212 () If lvcl211/ , 22, 22 then 1/vc221/1/vc vc 1/ vc 22 ct ct tt0, 0 , according to the formula m , we get: ct ct ct ct 2(ll12 ) 11 m 22 1/ vc221/ vc l llll Ⅱ 1 ， 1212 () If l2 22, 22 then 1/ vc22 1/vc221/1/vc vc 1/ vc 22 ct ct tt0, 0 , according to the formula m , we get: ct ct ct() ct ct ct 2(ll12 ) 1 1 m 22 1/ vc 1/ vc22 1 llll Ⅲ 22 2121 () If 1/vcll12 l 1, 22, 22 1/ vc22 1/vc1/vc22 1/ vc 22 1/ vc ct ct then tt0, 0 , according to the formula m , we get: ct ct ct ct 2(ll21 ) 11 m 22 1/ vc 1/ vc22 22 1 In Michelson’s experiment, ifll12 , but come close sufficiently, if 1/vcll12 l 1, 1/ vc22 to calculate according to the formula IV ct ct ct ct 2(ll21 ) 11 m 22 , m 0 , therefore, the 1/ vc 1/ vc22 interference stripe don’t move basically, so that the obvious movement of the interference stripe can’t be observed in the experiment. 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